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Dataplot Vol 2 Vol 1

MEDIAN ABSOLUTE DEVIATION

Name:
    MEDIAN ABSOLUTE DEVIATION (LET)
Type:
    Let Subcommand
Purpose:
    Compute the median absolute deviation for a variable.
Description:
    The median absolute deviation is:

      \( \mbox{MAD} = \mbox{median} |x - \tilde{x}| \)

    where \( \tilde{x} \) is the median of the variable. This statistic is sometimes used as a robust alternative to the standard deviation as a measure of scale.

    The scaled MAD is defined as

      MADN = MAD/0.6745

    For normally distributed data, the scaled MAD is approximately equal to the standard deviation.

Syntax 1:
    LET <par> = MEDIAN ABSOLUTE DEVIATION <y>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y> is the response variable;
                <par> is a parameter where the computed median absolute deviation is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Syntax 2:
    LET <par> = SCALED MEDIAN ABSOLUTE DEVIATION <y>
                            <SUBSET/EXCEPT/FOR qualification>
    where <y> is the response variable;
                <par> is a parameter where the computed scaled median absolute deviation is stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = MEDIAN ABSOLUTE DEVIATION Y1
    LET A = MEDIAN ABSOLUTE DEVIATION Y1 SUBSET TAG > 2
    LET A = SCALED MEDIAN ABSOLUTE DEVIATION Y1
Note:
    Dataplot statistics can be used in a number of commands. For details, enter

Default:
    None
Synonyms:
    MAD is a synonym for MEDIAN ABSOLUTE DEVIATION
    MADN is a synonym for SCALED MEDIAN ABSOLUTE DEVIATION
    NORMALIZED is a synomym for SCALED
Related Commands: Applications:
    Robust Statistics
Implementation Date:
    1995/04
    2016/02: Added SCALED MEDIAN ABSOLUTE DEVIATION
Program 1:
     
    LET Y1 = LOGISTIC RANDOM NUMBERS FOR I = 1 1 100
    LET A1 = MEDIAN ABSOLUTE DEVIATION Y1
    LET A2 = SCALED MEDIAN ABSOLUTE DEVIATION Y1
        
Program 2:
     
    SKIP 25
    READ GEAR.DAT DIAMETER BATCH
    TITLE AUTOMATIC
    XLIMITS 1 10
    MAJOR XTIC MARK NUMBER 10
    MINOR XTIC MARK NUMBER 0
    XTIC OFFSET 1 1
    X1LABEL BATCH
    Y1LABEL MEDIAN ABSOLUTE DEVIATION OF DIAMETER
    MAD PLOT DIAMETER BATCH
        
    plot generated by sample program

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Date created: 04/11/2016
Last updated: 04/11/2016

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